Appropriate Combination of Selection and Crossover Functions in Genetic Algorithm for Power System State Estimation

Determining the voltage magnitude and phase angle to evaluate the power system state is the problem of estimating the power system state. The studies on applying continuous genetic algorithms to deal with this problem are limited. Therefore, this research focuses on applying continuous genetic algorithms, which use selection, crossover, and mutation functions to produce new individuals for the next generation, to estimate the power system state. These functions have many different forms. The applied form of the function affects the results of the algorithm. Currently, there is no concrete research on the influence of these functions on estimation results of the power system state. Therefore, this article investigates how the combination of selection and crossover functions affects that problem. The selection functions studied in this paper are roulette wheel selection, rank weighting selection, and tournament selection. The crossover functions used are arithmetic crossover and heuristic crossover. The value of the state variable created from these two crossovers depends on the value of the coefficient β and how the crossovers process is performed. From there, the article considers three cases for each crossover: using a constant β coefficient in each cross pair, or using a variable β coefficient for each state variable in each crossover pair, or just performing partial crossovers. To find the best combination, 18 combinations of selection and crossover functions were simulated on 5-node and 14-node grids. The results show a clear difference between these and indicate that roulette wheel selection with the crossover heuristic is the most appropriate combination for the problem of estimating the value of the power system state variable.